Harris started acting as a youngster and attended New York's famed Juilliard School. After graduation from Juilliard's Drama Division, she joined John Houseman's touring repertory company The Acting Company, where she stayed for three years. During this time, she performed in productions of Shakespeare's King Lear and Romeo and Juliet, the classic Antigone, and alongside Frances Conroy in Bertolt Brecht's Mother Courage and Her Children.
Harris went on to do extensive work on and off-broadway including a 1989 performance at Second Stage Theatre in What a Man Weighs . One of Harris's breakthrough stage performance came in the original cast of Paul Rudnick's Jeffrey, where she was the sole female cast member. Her work in Jeffrey led to numerous television guest appearances, including a recurring role on the TV series Frasier as Frasier's conniving agent Bebe Glazer.
Harris received a Tony Award in 2002 as a Featured Actress in a Musical for playing the evil white slaver Mrs. Meers in Thoroughly Modern Millie.
In 2006 she appeared as Vera Charles in the Kennedy Center's summer production of Mame opposite Christine Baranski in the title role. In early 2007, Harriet appeared as Amanda Wingfield in the production of The Glass Menagerie at the Guthrie Theater. In the summer of 2007, Harriet appeared on Broadway in the revival of the John Van Druten comedy Old Acquaintance as Mildred Watson Drake with Margaret Colin at the American Airlines Theatre.